Answer:
AD = 3
BD = 10
CD = 17
Step-by-step explanation:
The requires side lengths are:
[tex]AD = \frac{49}{25}[/tex]
[tex]BD = \frac{168}{25}[/tex]
[tex]CD = \frac{576}{25}[/tex]
Considering triangle BDC, we have:
[tex]BC^2 = BD^2 +CD^2[/tex]
This gives
[tex]24^2 = BD^2 +(25 - AD)^2[/tex]
[tex]576 = BD^2 +(25 - AD)^2[/tex] --------- (1)
Considering triangle ABD, we have:
[tex]7^2 = BD^2 + AD^2[/tex]
[tex]49 = BD^2 + AD^2[/tex] ---- (2)
Subtract (2) from (1)
[tex]576 - 49 = BD^2 -BD^2 +(25 - AD)^2 - AD^2[/tex]
[tex]527 = (25 - AD)^2 - AD^2[/tex]
Expand
[tex]527 = 625 - 50AD + AD^2 - AD^2[/tex]
[tex]527 = 625 - 50AD[/tex]
Collect like terms
[tex]50AD = 625 - 527[/tex]
[tex]50AD = 98[/tex]
Divide both sides by 50
[tex]AD = \frac{98}{50}[/tex]
Reduce fraction
[tex]AD = \frac{49}{25}[/tex]
Recall that:
[tex]49 = BD^2 + AD^2[/tex]
So, we have:
[tex]49 = BD^2 + (49/25)^2[/tex]
[tex]49 = BD^2 + 2401/625[/tex]
Collect like terms
[tex]BD^2 = 49 - 2401/625[/tex]
Take LCM
[tex]BD^2 = \frac{625 *49 - 2401}{625 }[/tex]
[tex]BD^2 = \frac{28224}{625}[/tex]
Take the square roots of both sides
[tex]BD = \frac{168}{25}[/tex]
Also, we have:
[tex]CD = 25 - AD[/tex]
This gives
[tex]CD = 25 - \frac{49}{25}[/tex]
Take LCM
[tex]CD = \frac{625 - 49}{25}[/tex]
[tex]CD = \frac{576}{25}[/tex]
Hence, the requires side lengths are:
[tex]AD = \frac{49}{25}[/tex]
[tex]BD = \frac{168}{25}[/tex]
[tex]CD = \frac{576}{25}[/tex]
Read more about right triangles at:
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Please help quick will give brainly
Answer:
[tex]1134yd^3[/tex]
Step-by-step explanation:
Right Triangular Prism
V = LWH
L = 6yd
W = 21yd
H = 9yd
____________________
Follow the volume formula, and multiply the length by width and height together.
V = LWH
V = (6)(21)(9)
V = 1134yd^3
please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Area = 7.853981 in^2 (2.5 Pi)
Perimeter = 11.42478 in (3.63Pi)
Step-by-step explanation:
Area
Lg semi circle area = Pi(2^2)(0.5) = 3.141593(4)0.5) = 6.283185 in^2
Sm semi circle area = Pi(1^2)(0.5) = 3.141593(2)(0.5) = 1.570796 in^2
added together = 7.853981 in^2
Perimeter
Lg semi circle perimeter = Pi(4)(0.5) + 2 = 8.283185 in
Sm semi circle perimeter = Pi(2)(0.5) = 3.141593 in
added together = 11.42478 in
Solve the simultaneous equations
3x−2y=27
3x−y=24
x=? y=?
I can do this easily with positives but somehow I just don't understand a bit in negatives, can anyone help?
None of my answers are working.
Answer:
3x-2y=24 _____ (1)
2x-3y=18 _____ (2)
multiply (1) by 2
6x - 4y = 48
multiply (2) by 3
6x-9y=54
subtracting
6x - 4y = 48
6x - 9y = 54
- + -
___________
5y = -6
y=−
5
−6
3x−2(−
5
6
)=24
=3x+
5
12
=24
=3x=24−
5
12
=
5
120−12
=
5
108
∴x=
5
36
x+y=
5
36−6
=
5
30
=6
x−y=
5
36+6
=
5
42
solution
Step-by-step explanation:
according to me this should be the answer
good luck
hope it becomes helpful to you ☺️☺️
The x and y value from the given system of equations are 7 and -3 respectively.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given simultaneous equations are 3x-2y=27 ------(I) and 3x-y=24 ------(II) .
Subtract equation (I) from (II), we get
3x-y-(3x-2y)=24-27
⇒ y=-3
Substitute y=-3 in equation (I), we get
3x-2(-3)=27
⇒ 3x=21
⇒ x=7
Therefore, the x and y value from the given system of equations are 7 and -3 respectively.
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Question 9: emathintruction can you guys help me?
Answer:
Step-by-step explanation: answer 3
what's the area to this problem?
i dont know explain your?
Is every rhombus with four right angles is a square. True or False
Answer:
True.
Step-by-step explanation:
A rhombus has four side of the same length (sometimes) and bisecting diagonals.
A square has what a rhombus has, as well as what a rectangle has.
A rectangle has parallel sides, four right angles, and congruent diagonals.
That means that a square has four right angles, four sides of the same length, and bisecting diagonals.
That's why a square is a rhombus and a rectangle but not its converse.
So, true.
Every rhombus with four right angles is a square. Therefore, the given statement is true.
What is a rhombus?A rhombus can be defined as a special parallelogram as it fulfills the requirements of a parallelogram, i.e. a quadrilateral with two pairs of parallel sides. In addition to this, a rhombus has all four sides equal just like a square. That is why it is also known as a tilted square. Look at the image below to understand the relationship of rhombus shape with parallelogram and square.
A square is a quadrilateral with four equal sides. There are many objects around us that are in the shape of a square. Each square shape is identified by its equal sides and its interior angles that are equal to 90°.
Therefore, the given statement is true.
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I wanna do good on this plz help me!!
Answer:
2/1
Step-by-step explanation:
JA is the same side as KM
JA=24, KM=12
24/12=2
SOLVE WORD PROBLEM- Jane has $75 in her checking account. She will deposit $30 in her account each month. How many months will it take her to reach $345?
Answer:
Step-by-step explanation:
$345 - $75 = $270 more needed
$270 × (1 month)/($30) = 9 months
What is the Pythagorean Theorem. Please explain.
A bag contains orange and yellow sweets the ratio of orange to yellow sweets is 3:2 There are 51 orange sweets in the bag find the total number of sweets in the bag.
Answer: 34
Step-by-step explanation: the ratio is 3:2 we know that there are 51 orange sweets but we don’t know how many are yellow so the current ratio is 51:x we need to find x so if we divide 3 by 51 the answer is 17 so we need to multiply 17 by 2 which is 34 so x is equaled to 34 the final ratio is 51:34
hope it helped :)
if you get 0=0 is that no solution or IMS
looks like that would be ims
(4 x 1) + (0 x 1/10) + (7 x 1/100) + (6 x 1/1000)
Answer:
1019/250 x
Step-by-step explanation:
4x1+
0x1
10
+
7x1
100
+
6x1
1000
PLEASE SOMEONE HELP ME
( There are np answer choices)
Answer:
whhhhhh
Step-by-step explanation:
it is number 2 because i took the test
pls help me its due now
Answer:
answer : 90
Step-by-step explanation:
Answer:
90 m
Step-by-step explanation:
30% of 300 m =
= 30% * 300 m
= 0.3 * 300 m
= 90 m
PLS HELP GEO TEST 1, 2, and 3,
Answer:
it's blurry can't see it
Determine the value of the variable in each expression.
What is the value of m in the quotient of powers StartFraction 9 Superscript negative 3 Over 9 squared EndFraction = StartFraction 1 Over 9 Superscript m EndFraction?
m =
What is the value of n in the quotient of powers StartFraction x Superscript negative 4 Over x Superscript negative 6 EndFraction = x Superscript n
n =
What is the value of c in the quotient of powers StartFraction (negative 11) Superscript 7 Over (Negative 11) Superscript 0 EndFraction = (Negative 11) Superscript c
c =
Answer:
Step-by-step explanation:
m = 5
n = 2
c = 7
Answer:
5
2
7
Step-by-step explanation:
HELP QUICK!! solve by substitution and show work please
Answer:
(-1,-3)
Step-by-step explanation:
Substitute y=x-2 into y=4x+1
x-2=4x+1
substract -1 on both sides.
x-3=4x
subtract x on both sides
-3=3x
divide by 3 on both sides
x=-1
Substitute -1 into equation
y=x-2
y=(-1)-2
y=-3
So it would be (-1,-3)
Hoped it helped!
If you don’t know pls don’t answer
first row: multiply the numbers (on top of the yellow highlighted squares) by 2, then add one to it
second row: add 5 to the top numbers (top of the highlighted squares)
third row: multiply 8 by the top numbers (top of highlighted squares), and then subtract 4 by it
A rectangular-shaped parking lot is to have a perimeter of 458 yards. If the width must be 51 yards because of a building code, what will the length need to be?
Answer:
178 yards
Step-by-step explanation:
458-(51 times 2)
356/2
178
Help with one please last question free 10 points
Answer:
The triangles are similar
Step-by-step explanation:
The angles are all the same, except the big triangle was flipped and the unnamed angle in the small triangle is named in the other one
Answer:
The triangles are not similar because their angles measurements are not the same.
Step-by-step explanation:
Evaluate the following function for f(4). F(x)=2x-12
Estimate 1188+405+848 by first rounding each number to the nearest hundred
Answer:
about 2300
Step-by-step explanation:
Si tengo $ 86 pesos y compro 3 libros de 1 ! " cada uno y seis objetos de a $ # " cada uno, ¿cuánto me queda? R = 77 $ " � %!& "
Answer:
Originalmente tenés $86 pesos.
Compras 3 libros de " 1 ! " cada uno.
(voy a suponer que 1 ! es un valor)
Entonces tenés que pagar 3 veces el valor 1 !
Esto significa que ahora tendrás:
$86 pesos - 3*(1 !)
Y ahora compras 6 objetos de $# cada uno.
Entonces tenés que pagar 6 veces $#.
Esto significa que tenemos que restar 6*$# a lo que te quedaba, entonces ahora vas a tener:
$86 - 3*(1 !) - 6*($#)
Este será tu resto después de la compra.
PLEASE HELPPP
which of these choices are equivalent to the quotient below check all that apply square root of 100 over the square root of 20
Answer:
A
Step-by-step explanation:
Your sister is 2 yrs. Older than your brother. Their age combined is 30 yrs. What is your sisters age?
Answer:
the sister is 16
Step-by-step explanation:
30-14= 16 and thats a 2 year difference
Answer:
sister is 16
Step-by-step explanation:
explanation:
16+14=30
so the sister is 16 and the brother is 14. if that makes any sense ;)
what is the expression for this click the box thingy if you can't see it
Answer:
[tex]m^{12}[/tex]
Step-by-step explanation:
Cynthia besch wants to buy a rug for a room that is 18ft wide and 35ft long she wants to leave a uniform strip of floor around rug she can afford to buy 528 ft of carpeting what dimensions should rug have
Answer:
rug long = 34 ft
rug wide = 17 ft
Step-by-step explanation:
given data
wide = 18 ft
long = 35 ft
area of carpet = 528 ft
solution
we get here area of floor that is
and we consider length of carpet = 35 - 2x
and width = 18 - 2x
(35 - 2x) × (18 - 2x) = 528 ...................1
solve it we get
x = 25.5 and x = 1
we choose 1 ft. as the width of the strip
so rug long = 35 - 1 = 34 ft
and rug wide = 18 - 1 = 17 ft
Please helpppp. I have a Limited time!!!!!!!
Answer:
[tex] 5A+3B =\begin{bmatrix} 33 & 32 & 47 \\ 39 & -12 & 56 \\ 26 & 19 & 30\end{bmatrix}[/tex]
Step-by-step explanation:
[tex] A=\begin{bmatrix} 3 & 4 & 7 \\ 6 & - 3 & 7 \\ 1 & 5 & 6 \end{bmatrix} \: and \: B=\begin{bmatrix} 6 & 4 & 4 \\ 3 & 1 & 7 \\ 7 & - 2 & 0 \end{bmatrix} [/tex]
[tex] 5A=5 \begin{bmatrix} 3 & 4 & 7 \\ 6 & - 3 & 7 \\ 1 & 5 & 6 \end{bmatrix}, \: \: 3B=3 \begin{bmatrix} 6 & 4 & 4 \\ 3 & 1 & 7 \\ 7 & - 2 & 0 \end{bmatrix} [/tex]
[tex] 5A=\begin{bmatrix} 15 & 20 & 35 \\ 30 & -15 & 35 \\ 5 & 25 & 30 \end{bmatrix}, \: \: 3B=\begin{bmatrix} 18 & 12 & 12 \\ 9 & 3 & 21 \\ 21 & - 6 & 0 \end{bmatrix} [/tex]
[tex] 5A+3B =\begin{bmatrix} 15 & 20 & 35 \\ 30 & -15 & 35 \\ 5 & 25 & 30 \end{bmatrix} +\begin{bmatrix} 18 & 12 & 12 \\ 9 & 3 & 21 \\ 21 & - 6 & 0 \end{bmatrix} [/tex]
[tex] 5A+3B =\begin{bmatrix} 15+18 & 20+12 & 35+12 \\ 30+9 & -15 +3 & 35 +21 \\ 5+21 & 25-6 & 30+0 \end{bmatrix}[/tex]
[tex] \purple {\bold {5A+3B =\begin{bmatrix} 33 & 32 & 47 \\ 39 & -12 & 56 \\26 & 19 & 30 \end{bmatrix}}} [/tex]
PLEASE HELP! i’m having a hard time understand this.
Answer:
Here' a quick summary of the answers:
Question a: center = (3, 2), scale = 9 / 20
Question b: center = (8, -1), scale = 3
Question c: center = (6, 4), scale = 3 / 2
Question d: center = (5, 3), scale = 2
Step-by-step explanation:
By "find the center of dilation", they're asking you to name the x/y point at which the image is scaled from.
The scale factor is the amount that the points are being scaled by to reach the "prime" of them (noted by the apostrophe). e.g., A would be the original point, and A' would be the transformed one.
To answer these, we'll need to pay careful attention to the coordinates in the graph. To get the scale, you can simply look at the equivalent side on both triangles, and compare the lengths.
In question A for example, we can see the line AC is 10 units wide, and the equivalent line A'C' is 4.5 units wide. This tells us that the triangle was scaled down by a factor of 4.5/10, or 9/20, or 45%
Finding out the center of dilation can be slightly more complicated. Note that there may be an easier way to do this that I am personally unaware of, but one way to do it would be to take the original and transformed versions of two points, e.g. A and A', and B and B', and use those points to define lines. We can then find where those lines intersect, and that tells us where the point of origin is.
Question A:
For example, in question A, the points A and A' are at (7, 4) and (5, 3) respectively. Remember that the slope of a line is equal to rise over run. In other words
s = (Ay - A'y) / (Ax - A'x)
s = (4 - 3) / (7 - 5)
s = 1/2, or 0.5
Now we can take that slope, and either of the the two points we used, and apply it to a point to define a line, using the formula Δy = sΔx
y - Ay = s(x - Ax)
y - 4 = 0.5(x - 7)
y = 0.5x - 3.5 + 4
y = 0.5x + 0.5
That gives us the line along which point A was translated when the triangle was scaled. Now let's find the same for point B:
s = (By - B'y) / (Bx - B'x)
s = (1 - 0) / (4 - 5)
s = 1 / -1
s = -1
And apply that slope to build our line:
y - By = s(x - Bx)
y - 0 = -1(x - 5)
y = -x + 5
Now that we have two lines created, we can simply equate them, solving for x, which tells us the x location of the center of dilation.
Given:
y = -x + 5
and
y = 0.5x + 0.5
we can say:
-x + 5 = 0.5x + 0.5
-2x + 10 = x + 1
-3x = -9
x = 3
So the center of dilation has an x coordinate of 3. To find it's y coordinate, we merely need to plug that into one of the line equations we already worked out:
y = -x + 5
y = -3 + 5
y = 2
So for question A the center of dilation is at (3, 2)
Question B:
This one is actually much easier, as we don't need to work out line equations to find the point of origin. The thing to notice here is that A and A' have the same x coordinate, forming a vertical line. Also B and B' have the same y coordinate, forming a horizontal line. All we need then is to know where those lines intersect. We can get that by taking the x coordinate of A and the y coordinate of B.
A lies at (8, 0), and B lies at (5, -1), so the center of dilation is (8, -1)
Using the same logic as above to find the scale, we get a scale of 3. This is easiest by comparing |CA| with |C'A'|, the left sides of the triangles. As you can see, that side is scaled up by a factor of 3.
Question C:
This one is far easier, as it is very obvious from the image that point A, at (6, 4) is the point of dilation. Using the same technique as above we can see that the scale is 3/2, or 1.5
Question D:
Again much easier, as we can see that the point of origin is on the halfway point of the side CA, (5, 3). Using the same method as above, we can see that the scale is 2.
I need help for 2,3, and 4
Answer:
2.x = -1 , y = 4
3.
x = 7, y = -1
4.
x = 1, y = 2
Step-by-step explanation:
2. 6x + 2y = 2, -3x - 4y = -13
3. 4x + 8y = 20, -4x + 2y = -30
4. y = -3x + 5, 5x - 4y = -3
2.We have to determine the solutions of this system of equations, basically look for x and y. First, let's solve through elimination.
6x + 2y = 2
-3x - 4y = -13
Multiply the second equation by 2 :
6x + 2y = 2
-6x - 8y = -26
Add the equations and solve for y :
-6y = -24
Divide both sides by -6 :
y = 4
Now that we have found y, we can substitute 4 in y of the first equation :
6x + 2(4) = 2
6x + 8 = 2
Subtract 8 from both sides :
6x = -6
Divide both sides by 6 :
x = -1
3.
4x + 8y = 20
-4x + 2y = -30
We are asked to solve in elimination style, do as followed :
4x + 8y = 20
-4x + 2y = -30
Add and solve for y :
10y = -10
Divide 10 from both sides to get y alone :
y = -1
Now that we know y, we can substitute it into the first equation :
4x + 8(-1) = 20
4x - 8 = 20
Add 8 to both sides :
4x = 28
Divide 4 from both sides :
x = 7
4.
y = -3x + 5
5x - 4y = -3
We are asked to solve with substitution :
Since the first equation has y alone, we can replace it with y in the second equation :
5x - 4(-3x + 5) = -3
Distribute :
5x + 12x - 20 = -3
Combine like terms :
17x - 20 = -3
Add 20 to both sides :
17x = 17
Divide 17 from both sides :
x = 1
Now that we know y, we can substitute x in the first equation with 1 :
y = -3(1) + 5
y = -3 + 5
y = 2